How can I translate parts of mesh without affecting the hidden part?
Not really, that's what you get for not looking at everything that you are transforming. Think of it like this:


Vertices are "linked" to every edge that they are attached to (duh).
Edges are "linked" to every face that they are attached to.
Faces are "linked" to each other through edges.


This is the fundamental problem...if you move a vertex, edge, or face with some of the "components" that it is linked to hidden, Blender has no choice except to move those along with it. Blender's mesh tools act no differently with things hidden or not; it is simply a way to get unnecessary parts of the mesh out of your way. You should only really be hiding things that won't be affected by your editing (i.e., only hide things that are relatively far away from the area you are changing).